Page 290 - Improving Machinery Reliability

Life Cycle Cost Studies 261

troubleshooting and component replacement costs are again estimated at $3,700.
Although the projected MTTR is 4 hours, the probable MTBR of this active redun-
dant system is 9.16 + (9.16/2) = 13.74 years.* Prorated expenditures attributable to
flare Bosses, lost profits, restart expenses, overtime, and environmental fines will be
again $106,600 resulting in annual costs of 106,600/13.74, or $7,758.
The total life cycle cost for each option can now be obtained by adding the initial
acquisition cost, the initial installation cost, and the recurring yearly costs. A present
value conversion accounts for the time value of money and allows future operations
(OC), maintenance (MC), lost production (LP), and even decommissioning costs
(DC) to be added to present acquisition and installation costs. The total life cycle
cost (LCC Total) is thus:

= AC + IC + present value of (OC + MC + LP + DC) Reference 3
Present value is cost multiplied by the cumulative present worth factor
I i(1 + i)" J (5 - 2)
(1 + i)"
- 1

where: i = seal annual interest rates in percent, and
n = number of years

The factor may be obtained from tables as a function of interest rate and time
(years), but it is also readily available on most computer spreadsheet programs as a
present value (PV) function.
For the various options, using annual interest rates of 6%, and projecting a 30-year
plant life, we would obtain present values of $267,024; $209,881; and $178,659,
respectively.
Total life cycle costs would be $267,024 for option 1; $209,881 for option 2; and
$178,659 for option 3. The redundant electronic governor option would thus be favored.

How to Obtain Data on Failure Frequencies

.Anticipated failure frequencies and life expectancies of machinery and compo-
nents are not always readily available. Nevertheless, an experienced reliability pro-
fessional will not be deterred in his search for data. He or she may resort to a tele-
phone survey of known users, communicate with the service departments of original
manufacturers and repair shops, engage in literature search in a technical library, or

*MTBF of a randomly failing multiple component active redundant system may be evaluated
, where the failure rate h = - = number of parallel
c
and
MTBF'
components.